Learning Backgammon

In Skill and Luck in Backgammon, I described the process by which I settled on the parameters tourneygeek should use to simulate backgammon tournaments. The result was that the luck factor should be set to three, which implies that backgammon is 75% luck, and only 25% skill.

This does not mean, however, that backgammon is an easy game – a game in which a few small, easily learned heuristics will allow you to play at a high level. Open any of the many more advanced monographs on backgammon strategy and tactics, and you’ll soon see that there’s an enormous body of knowledge that expert players have and others do not. There’s plenty of skill in backgammon, it’s just that this skill is regularly overwhelmed because there’s even more luck.

How do players learn the game under these conditions? This post will examine two reasons that the high degree of luck makes good backgammon difficult to learn.

The Double-Six Rule

Let’s begin with a familiar heuristic of backgammon play, one that’s known to essentially all intermediate players:

When your opponent is closed out, and you are bearing in the rest of your checkers, try to move so that rolling a double six on your next turn does not cause you to leave a shot.

I apologize to readers who don’t play backgammon – let me tell you what this rule means in practical terms:

In a fairly common position, you’re way ahead and a heavy favorite to win the game. But a particular sequence of dice throws can turn the tables. The likelihood of this happening is (1/36) * (11/36), or about 0.85%. Don’t let this happen if you can help it.

This is an exceptionally difficult rule to learn simply by playing a lot of backgammon. You can go for weeks and months blithely ignorant of the double-six rule, and nothing bad will happen. And sometimes, when something bad does happen, you couldn’t have done anything about it. But eventually you’ll lose a game through ignorance of the rule, and (though it may not feel this way at the time) it will be a kindness if your opponent takes the opportunity to teach it to you. In all likelihood, you’ll forget, and the rule won’t really stick in your mind until this has happened to you not just once, but a few times.

Backgammon is hard to learn exactly because the luck of the dice so often submerges skillful play. You’re rewarded for making the wrong move nearly as often as you are rewarded for making the right one.

Another reason that the double-six rule is difficult to learn is that it requires you to act contrary to the habits you’ve established. When you are in a commanding position, you have the luxury of worrying about the baleful effects of one particular unlikely sequence of dice throws. When you are way behind, you try to create a situation in which such a sequence will rescue your awful position. But in the great in-between region, there are simply too many possibilities to account for. In these complex, more balanced positions, your moves are governed more by a feeling you’ve developed for the game. Some positions simply look better than others, and the double-six rule will often call for a move that you’ve taught yourself to see as a bit ungainly.

Who’s Ahead?

Good backgammon players develop a sort of aesthetic sense for the quality of a position, and supplement that with a number of heuristics like the double-six rule. These are often sufficient to guide the player to the right play. But in backgammon, it is frequently necessary not just to know what the right play is, but to know how right it is.

People attending their first cricket match are prone to asking, in all innocence, “who’s ahead?” without realizing that this is often a very awkward question. In cricket, it’s very hard to know which team is ahead. The experienced fan doesn’t want to appear so ignorant as not to know who’s ahead, but the fact of the matter is that often they don’t know. There are a number of plausible techniques for answering the question, but they all have flaws, and many experienced fans have learned that trying to work out who’s ahead, and why, is usually less fun than just watching the cricket.

In backgammon, it can be similarly difficult to say who’s ahead, and by how much. But the use of the doubling cube frequently requires the player to make a reasonably accurate judgment about the chance of winning. The actual future course of the game is often all but impossible to predict because it is heavily dependent on the roll of the dice. And the proper strategy for both doubling and play can depend on the match score. A match score of 9-8 may call for a very different strategy than a score of 9-9.